Problem: Simplify the following expression: $\sqrt{208} - \sqrt{117}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{208} - \sqrt{117}$ $= \sqrt{16 \cdot 13} - \sqrt{9 \cdot 13}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{13} - \sqrt{9} \cdot \sqrt{13}$ $= 4\sqrt{13} - 3\sqrt{13}$ Finally, simplify by combining the terms. $= ( 4 - 3 )\sqrt{13} = \sqrt{13}$